Variation-perturbation treatment of the molecular interaction energy in H2+

Abstract

A new variation‐perturbation method is developed to treat the interatomic interactions in one‐electron diatomic molecules at all distances. For a diatomic molecule with nuclear charges Z_a and Z_b a variable charge‐shifting perturbation is defined as (Z_b − ζ)/r_a − Z_b/r_b, where r_a and r_b are the distances from the electron to the two nuclei. The adjustable parameter ζ, when determined variationally, leads to a small perturbation at all distances. Limiting cases are ζ = 0 and ζ = Z_b at zero and infinite separations, respectively. The method is tested by calculations of the ground‐state energy of the hydrogen molecular ion, for which the first‐order wavefunction is obtained in closed form. Following the procedure of Chang [J. Chem. Phys. 59, 1790 (1973)], both one‐ and two‐center calculations are performed. The results compare favorably with the exact values and converge correctly to the appropriate united‐ and separated‐atom limits. The largest deviation occurs near the equilibrium distance, where the relative error of energy, in the case of two‐center treatment, is 0.6%. Several other variational calculations are reported using various united‐ and separated‐atom functions as the basis set. Extension of the perturbation method to HeH⁺ is briefly discussed.